Devices for detecting a selvage of a material web or the selvage position in one measuring direction equipped with several ultrasonic sensors have been known, comprising a transmitter element and a receiver element having a circular shape, such as disclosed, for example, in DE 195 00 822. Providing a sufficiently large measuring range in the measuring direction requires in the case of these devices a larger number of ultrasonic sensors and more space, which increases the costs of the device as well.